WTA filter algorithm and coefficient design

Reconstruction filters and timing

Answers on this topic

• Is the filter algorithm more important than the tap count, and would more than a million taps keep improving the sound?
• What is the WTA filter, how was it tuned, and how does it differ from a conventional windowed sinc filter?

Everything he said on this topic (176)

One-line summaries in our words, oldest first. Each link opens the original.

• 2014-04-15Watts says Hugo's DAC is a pulse array with a 104 MHz noise shaper, the DPLL eliminates source jitter, and more taps keep helping, guessing 1M taps for 16-bit accuracy. Head-Fi, Apr 2014
• 2014-04-16Watts compares QBD76's 16-element pulse array with Hugo's 4, says a replacement is in work, and recounts how QBD76 development reshaped the WTA filter to 18k taps. Head-Fi, Apr 2014
• 2014-05-22Watts explains FIR taps and WTA coefficients, says perfect reconstruction needs infinite taps, and that Hugo's 26,368 taps run on 16 parallel DSP cores at 208 MHz. Head-Fi, May 2014
• 2015-06-18Watts explains the pulse array's analog-like distortion, why half-band filters keep original samples, and how a 256-tap WTA beat a 2048-tap half-band Kaiser filter in the late 90s. Head-Fi, Jun 2015
• 2015-11-22Watts says not to upsample on a computer before his DACs; Dave's 166 DSP cores outpace a PC, and only the WTA algorithm targets transient timing errors. Head-Fi, Nov 2015
• 2016-01-25Watts says he would not design a DAC without his WTA filter, which he has used since 1999 with the DAC64. Head-Fi, Jan 2016
• 2016-03-07Author says Chord's digital filter is the WTA filter, for Watts Transient Aligned, and quotes Watts that conventional DACs cannot completely restore the original analog signal. article, Mar 2016
• 2016-04-10Watts says the WTA algorithm uses his own windowing of the ideal sinc response, fine-tuned by listening, and that the Blu's impulse response would reveal its coefficients. Head-Fi, Apr 2016
• 2016-04-10Watts says a built-in impulse detector switches the WTA filter out when it sees an impulse, which music cannot trigger, and that the windowed coefficients are fixed in the FPGA. Head-Fi, Apr 2016
• 2016-05-17Watts says ringing never explained differences he heard tuning WTA, an ideal filter must ring, 8FS and 16FS filters with identical ringing sound different, and ADC ringing likely matters little. Head-Fi, May 2016
• 2016-07-24Watts says longer taps with normal filters on DAC64 changed the sound greatly, but refining the filter algorithm improved timing accuracy, leading to WTA and a tenfold improvement in sound. Hifistatement 1:39
• 2016-07-24Watts says WTA stands for Watts Transient Aligned. Hifistatement 2:24
• 2016-07-24Watts says WTA aims to align transients to the original recording, was fine-tuned through thousands of listening tests, and a 256-tap WTA beat a 2000-tap conventional filter. Hifistatement 2:28
• 2016-08-09Watts explains why a PC cannot replicate DAVE's processing: FPGAs run filter taps in parallel (DAVE 166 DSP cores, Mojo 44 at 0.45 W), and algorithm design also matters. Head-Fi, Aug 2016
• 2017-01-15Watts recounts M scaler development and CES demos, discusses judging the scale of changes, lists gains in timbre, bass pitch and depth, and describes improving stop-band rejection. Head-Fi, Jan 2017
• 2017-01-23Watts says Dave's 26,000 to 164,000 tap step disappointed him, algorithm and 16FS mattered more, 0.5M taps was transformational, and explains reducing errors until inaudible with a biscuit-barrel analogy. Head-Fi, Jan 2017
• 2017-02-10Watts says both tap count and algorithm matter; in the 1990s a non-aliasing filter became the first WTA, and a 256-tap WTA beat a 2048-tap conventional filter. Head-Fi, Feb 2017
• 2017-02-13Watts defends his Mojo timing illustration as a simplification, targets non-linear timing uncertainty rather than ringing, says doubling taps halves the error, and notes WTA accommodates half-band decimation. Head-Fi, Feb 2017
• 2017-02-14Watts says the likely lesson is how far decimation and interpolation are from transparency, and doubts Davina-sourced recordings would change the WTA algorithm, though future gains may follow. needs context Head-Fi, Feb 2017
• 2017-10-13Watts says reconstruction depends on two things, tap length and the coefficient algorithm, and explains that simply truncating a sinc function is a rectangular window. miceblue425 14:32
• 2017-10-13Watts says a windowing function tapers the truncated sinc, and his WTA window is optimized to reconstruct timing, refined over 20 years through perhaps thousands of listening tests. miceblue425 15:15
• 2017-10-13Watts says the filter algorithm hugely influences performance, and that around 1998 FPGAs could barely run an FIR filter; he needed three of them. miceblue425 20:34
• 2017-10-13Watts says doubling a Kaiser filter's tap length always improved bass, soundstage and timbre, but with no hope of more than a thousand taps he sought a better algorithm. miceblue425 21:21
• 2017-10-13Watts says his revised algorithm gave a tenfold improvement, a 256-tap WTA filter beating a 2000-tap Kaiser, yet going from 256 to 1000 WTA taps still helped. miceblue425 22:06
• 2017-10-13Watts says the 512,000-tap filter compared with DAVE gave his biggest shock in 5 years, partly due to an improved WTA filter and moving from 8FS to 16FS. miceblue425 30:21
• 2017-10-19Watts confirms the WTA window forces coefficients beyond 1.4 seconds to zero, and the ignored sinc coefficients are much smaller than 16 bits, giving better than 16-bit accuracy. Head-Fi, Oct 2017
• 2017-10-20Watts says an infinite sinc needs infinite processing, more taps reconstruct timing better, yet the algorithm matters too; he spent much time adjusting WTA to beat conventional filters. Hifistatement 51
• 2017-10-20Watts says a 2000 tap Kaiser filter sounds worse than a 256 tap WTA filter, but with a given algorithm more taps always gave better sound in his tests. Hifistatement 1:43
• 2017-10-28Watts says going from Hugo's 26k to DAVE's 164k taps changed little until WTA algorithm tweaks did; for a given algorithm, doubling taps doubles accuracy against the ideal. Head-Fi, Oct 2017
• 2017-11-15Watts says the M scaler's WTA coefficients match an ideal sinc to 16 bits, needing about 1 million taps and the right algorithm, which PC up-samplers lack. Head-Fi, Nov 2017
• 2017-12-02Watts says sampling theory only requires bandwidth limiting, which may use a non-pre-ringing IIR filter; his pre-ringing remark concerned DAC interpolation filters, and coefficient calculation matters beyond tap length. Head-Fi, Dec 2017
• 2017-12-02Watts says WTA optimizations improved every recording consistently, so the rule is to get as close to an ideal sinc as possible even for recordings with aliasing or ringing. Head-Fi, Dec 2017
• 2017-12-16Watts says DAC64 split WTA and pulse array across FPGAs, and stresses the WTA algorithm, coefficient quantizing and internal truncation as more important than raw tap length. Head-Fi, Dec 2017
• 2017-12-26Watts says his WTA filters roll off very fast: 49,152 taps reach -1dB within 75Hz of FS/2, the M Scaler's 1M taps within 4Hz, matching ideal sinc beyond 16-bit accuracy. Audiophile Style, Dec 2017
• 2017-12-27Watts says longer filters only help if accuracy against the sinc doubles with each doubling of taps; most algorithms differ too much from ideal sinc values to benefit. Head-Fi, Dec 2017
• 2018-01-18Watts says the 49,152-tap WTA 1 matches an ideal sinc to 12 bits, its coefficients diverging below that level; with the M scaler divergence occurs beyond 16 bits. Head-Fi, Jan 2018
• 2018-02-23Watts says 16-bit sinc accuracy needs a million taps, impossible in the 1990s, so he used listening tests to optimize his algorithm to recover timing more efficiently. MajorHiFi 9:17
• 2018-02-23Watts says a 256-tap WTA filter sounded better than a 2048-tap conventional half-band filter, at least a 10 to 1 improvement from the algorithm itself. MajorHiFi 10:05
• 2018-03-08Watts gives sinc-equivalent accuracy as 12.2 bits for Hugo 2, 13.9 bits for Dave and 16.6 bits for the M scaler, below which WTA coefficients diverge from the ideal sinc. Head-Fi, Mar 2018
• 2018-07-18Watts recounts WTA development from 1980s sinc ideals, finding sinc closeness beat image rejection alone, and wonders whether Davina's alias-free decimation will change the importance of tap length. Head-Fi, Jul 2018
• 2018-07-21Watts says conventional filters use only a few hundred taps because designers check only frequency response without listening tests, and he realized the algorithm could use resources better. c w 13:12
• 2018-07-21Watts says his WTA algorithm beat a conventional filter with a tenth of the taps, was fine-tuned through thorough listening tests, and needed changes as tap length grew. c w 13:58
• 2018-07-21Watts calls WTA a unique windowing function applied to the sinc, and starts a tap-length history: DAC64 in 1999 had a thousand taps using three FPGAs and 15 watts. c w 14:48
• 2018-07-21Watts says a million taps now run at the same power as DAC64's thousand in 1999, and at a million taps the WTA coefficients become identical to a sinc function. c w 18:36
• 2018-07-26Watts says the M scaler needs bit-perfect input because PC upsamplers lack the processing power and a sinc-like WTA algorithm; its SPDIF output is asynchronous but the DPLL is transparent. Head-Fi, Jul 2018
• 2018-07-26Watts posts his CanJam presentation: transients cue placement, pitch and timbre; conventional filters mistime them; 1M WTA taps match sinc to 16.6 bits using 528 DSP cores. Head-Fi, Jul 2018
• 2018-07-27Watts explains dual-data and DX modes, M scaler DSD-to-PCM conversion with Hugo 2's 220 dB filter, says algorithm beats tap length, and compares R2R and delta-sigma timing errors. Head-Fi, Jul 2018
• 2018-08-03Watts says a standard PC lacks the CPU power for 1M taps though a GPU PC could, but it still would not be the WTA algorithm, which matters most. Head-Fi, Aug 2018
• 2018-08-06Watts says he spent a lot of time fine-tuning the filter to get the best sound on the Blu, and once that project was sealed it should not be changed. Pursuit Perfect System 5:55
• 2018-08-19Watts says a claimed 10,000,000-tap filter has a very poor transition band that a few thousand taps could match; Mojo's WTA is 10 times better, and algorithm beats tap length. Head-Fi, Aug 2018
• 2018-08-19Watts posts a quickly made 10M-tap conventional Kaiser filter with a transition band under 2 Hz, over 1000 times sharper than the test file. Head-Fi, Aug 2018
• 2018-10-31Watts explains WTA1's 768 kHz output as a listening-test balance, WTA2's 256FS step shared by all current DACs except Mojo, and a three-stage IIR filter to 9.6 nS. Head-Fi, Oct 2018
• 2018-12-07Watts says the 4x (48 to 192 kHz) filter uses exactly a quarter of the 16x coefficients, not a decimation, and is volume adjusted with near-Gaussian 24-bit dither. Head-Fi, Dec 2018
• 2018-12-13Watts says the algorithm strongly affects sound: his first WTA filter in 1999 used a thousand taps, the FPGA limit, versus 100 conventionally, and algorithm changes improved transients. Pursuit Perfect System 6:44
• 2018-12-13Watts says the WTA algorithm was refined from theory and hundreds of listening tests, so that a 256-tap WTA filter sounded better than a 2048-tap conventional filter. Pursuit Perfect System 7:30
• 2018-12-13Watts claims a tenfold reconstruction gain without more taps, says half the WTA coefficients are identical to an ideal sinc function, and says sinc-like filters sound more natural. Pursuit Perfect System 8:20
• 2018-12-17Watts says 2 V is 3.5 dB and 1 V 9.5 dB below 3 V; non-WTA upsamplers cannot predict the M Scaler, as longer conventional filters add near-zero coefficients. Head-Fi, Dec 2018
• 2019-04-19Watts defines tap length, explains the WTA window leaves just over half the coefficients exactly sinc, guaranteeing reconstruction better than 16 bits, and notes a typo in Keith Howard's article. Head-Fi, Apr 2019
• 2019-04-22Watts says the filter uses direct, fixed-point convolution with noise-shaped coefficients, explains FFT convolution, and expects sound differences between them; output truncation also matters. needs context Head-Fi, Apr 2019
• 2019-09-10Watts says doubling WTA taps adds one bit of sinc accuracy, and 88.2/96k input runs the same coefficients as an 8-times filter, keeping accuracy and processing unchanged. Head-Fi, Sep 2019
• 2019-09-14Watts says the industry misunderstands reconstruction, so minimum phase, NOS and no-ringing filters worsen timing, and fitting sinc to finite processing by listening and custom windowing is the real work. Head-Fi, Sep 2019
• 2019-10-14Watts says all his WTA filters include overload headroom for Gibbs and inter-sample overshoot, but the changes observed have many subtle causes affecting instrument separation. needs context Head-Fi, Oct 2019
• 2019-12-19Watts says others use standard maths-based filters such as Kaiser, that an abruptly truncated sinc sounds bad, and that how the taper is done matters. Passion for Sound 23:37
• 2019-12-19Watts says WTA was shaped by the maths, removing image aliasing, and hundreds of listening tests tuning the taper; his first test pitted 256-tap WTA against 2,000-tap Kaiser. Passion for Sound 24:25
• 2019-12-19Watts says the 256-tap WTA filter sounded much better than the 2,000-tap Kaiser filter, at least a tenfold improvement in transient reconstruction. Passion for Sound 25:10
• 2020-01-27Watts says dual-BNC 768k on Mojo was dropped in 2015 to save power and the manual corrected; Mojo takes 768k on USB, and the algorithm matters more than tap length. Head-Fi, Jan 2020
• 2020-06-25Watts says DAVE used a three-stage filter from 768 kHz up to 104 MHz, and he experimented replacing part of it with a WTA filter outputting every 1.6 microseconds. Part-Time Audiophile 23:30
• 2020-11-11Watts compares 1M-tap rectangular sinc, Kaiser and WTA filters by measurement and listening, explains how the WTA equation was tuned, and concludes algorithm matters more than tap length. Head-Fi, Nov 2020
• 2020-11-14Watts says an infinite-tap sinc guarantees correct intermediate values for bandlimited signals, and WTA is far more accurate per tap, with doubling taps doubling accuracy; improvement has not yet converged. Head-Fi, Nov 2020
• 2020-11-27Watts advises never upsampling before his DACs and says M Scaler research at 1M taps showed the WTA algorithm is 50 to 500 times more effective than conventional filters. Head-Fi, Nov 2020
• 2020-11-27Watts says to avoid all up-samplers unless they contain a WTA filter, since WTA optimization through listening tests matters much more than tap length. Head-Fi, Nov 2020
• 2021-06-04Watts says what matters is how many taps are Whittaker-Shannon, about 256M for 24-bit recovery; windowed or apodized sinc fails, and 64-bit float causes noise floor modulation. Head-Fi, Jun 2021
• 2021-09-09Watts says a 768kHz signal has 256 times less transient error area than 48kHz, why higher rates sound better, and his WTA tuning found one sweet spot across recordings. Head-Fi, Sep 2021
• 2021-10-03Watts says WTA tuning balanced image attenuation against sinc-like transient reconstruction through thousands of listening tests, and that out-of-band images also cause transient timing errors. Head-Fi, Oct 2021
• 2021-11-30Watts says correct filter timing errors are amplitude independent but transients intermodulate through non-sinc windows; a WTA simulation matched 0dBFS and -301dB, and coefficient accuracy improved depth. Head-Fi, Nov 2021
• 2021-12-06Watts says HQPlayer and PGGB give no idea of M scaler performance, since many taps with the wrong algorithm give the wrong result, and only WTA minimizes transient timing error. Head-Fi, Dec 2021
• 2021-12-23Watts says the only subjectively important job of an interpolation filter is reconstructing transient timing, that other designers ignore it, and that thousands of listening tests tuned WTA. Head-Fi, Dec 2021
• 2022-02-11Watts says his high-end M Scaler uses a Choral (DAVE) chassis and is not 4M taps, algorithm outweighs taps, and gives SINAD of 125dB (Mojo 2) and 127dB (TT2). Head-Fi, Feb 2022
• 2022-03-19Watts says the WTA filter makes the best of limited processing, began in 1999 with DAC64 at a thousand taps, and explains what a tap is. MFG Audio Reviews 21:09
• 2022-03-19Watts says doubling taps with the same algorithm doubles reconstruction accuracy, the ear is extremely sensitive to timing errors, and the WTA filter was optimized by many listening tests. MFG Audio Reviews 22:03
• 2022-03-19Watts says WTA was tuned mostly by listening, down to ten parts per million on the windowing function, and Mojo 2 has over 500 times a chip DAC's processing. MFG Audio Reviews 22:49
• 2022-04-26Watts says the WTA filter minimizes timing modulation but cannot eliminate it, nor can an M Scaler; his algorithm maximizes accuracy with limited taps, and Mojo's FPGA is custom coded. Audio Force 11:37
• 2022-05-03Watts says a brick-wall filter would reconstruct transients perfectly, the WTA filter approximates it via thousands of listening tests, and its optimum is recording-independent because timing error is structural. Head-Fi, May 2022
• 2022-05-05Watts says the most accurate transient reconstruction needs symmetric windowing; he uses asymmetric windowing only in video mode, gaining lower latency at a sound-quality price. Head-Fi, May 2022
• 2022-07-25Watts says the WTA windowing function shown does not resemble the real one, which he has never published and will not describe. Head-Fi, Jul 2022
• 2022-08-19Watts says a disclosed scaler to match DAVE, three or four years in work and priced like DAVE, won't replace the Hugo M Scaler; more taps help, but algorithm matters. AVstore 7:51
• 2022-08-19Watts says every upsampler contains a filter, even NOS (a first-order hold), and the two key factors are the number of taps, which sets reconstruction accuracy, and the algorithm. AVstore 14:39
• 2022-08-19Watts says the algorithm calculates the coefficients and is free to design, while tap count is limited by hardware, since each tap needs memory, a multiplier and an accumulator. AVstore 15:27
• 2022-08-19Watts says the upsampling filter is an FIR filter based on a sinc function, which rings to infinity in past and future, so its ends must be chopped off. AVstore 16:15
• 2022-08-19Watts says a windowing function tapers the sinc to zero, how the tapering is done is crucial, and in his filter more than 50% of coefficients are ideal sinc values. AVstore 16:58
• 2022-08-19Watts says not all coefficients can be ideal, so his own five-variable windowing function balances gentle tapering against maximizing ideal values, each variable tuned by listening. AVstore 17:43
• 2022-08-19Watts says he tunes each variable listening for separation and focus, soundstage depth, timbre, bass pitch (dependent on transients), and the starting and stopping of notes. AVstore 18:29
• 2022-08-19Watts says digital makes a wood block crack sound softer, that note starts and stops depend on transients, and optimizing five interacting variables took thousands of listening tests. AVstore 19:17
• 2022-08-19Watts says listening tests optimized his windowing function to within ten parts per million, and that while taps are very important, how the filter is designed is absolutely crucial. AVstore 20:01
• 2022-08-19Watts agrees, saying lots of taps with a conventional algorithm will not sound good. AVstore 20:56
• 2022-08-21Watts says WTA uses five variables tuned by thousands of listening tests, the algorithm matters more than tap length, and a two-sample linear interpolation filter would be a disaster. Head-Fi, Aug 2022
• 2022-09-18Watts says the WTA algorithm that sets the M Scaler's WTA filter uses his equations with five variables, which are listened to, modified and honed to a sweet spot. The Source AV 22:00
• 2022-09-18Watts says the sweet spot is set to within 10 parts per million by listening for separation, timbre, bass pitch and soundstage, adjusting each variable and rechecking the others. The Source AV 22:30
• 2022-09-18Watts says the WTA algorithm took thousands upon thousands of listening tests with specific tracks. The Source AV 23:15
• 2022-10-12Watts says it creates harmonic and anharmonic distortion, calls the latter really nasty, and says only the WTA filter is designed to minimize these; the M Scaler adds computing power. Upscale Audio 3:50
• 2022-10-12Watts says the M Scaler improves performance, and that improving transient reconstruction accuracy through the filter's design took thousands of listening tests. Upscale Audio 4:25
• 2022-10-12Watts says the filter design has five coefficients, each fine-tuned by literally thousands of listening tests to an accuracy of 10 parts per million. Upscale Audio 4:43
• 2022-10-12Watts describes scoring each coefficient on half a dozen tracks for timbre, pitch, instrument separation and focus, depth and soundstage, then rechecking earlier coefficients. Upscale Audio 5:10
• 2022-10-12Watts says the WTA filter has been around a long time and is successful with studios as well as audiophiles. Upscale Audio 5:55
• 2023-02-04Watts says 1000 taps fell far short of the million needed for 16-bit accuracy, so he looked at changing the coefficient algorithm instead of standard Kaiser or other windows. Dusty Audio 42:07
• 2023-02-04Watts says the WTA algorithm, a formula with five functions, was tuned over 25 years by thousands of listening tests scoring pitch, depth, separation and timbre. Dusty Audio 42:48
• 2023-02-04Watts says others use standard math and trust their brand; with the M Scaler's million taps he can guarantee 16-bit reconstruction accuracy between samples. Dusty Audio 43:46
• 2023-02-05Watts says that was the first WTA filter. needs context Soundnews 19:45
• 2023-03-26Watts says the limit is reached when doubling taps is inaudible; during Covid he investigated it while working on a scaler to match DAVE, stressing reconstruction accuracy over taps. Eric's Hi-Fi 3:09
• 2023-03-26Watts says his WTA windowing function has five variables, each with a sweet spot found by listening and adjusting, to an accuracy of about ten parts per million. Eric's Hi-Fi 3:55
• 2023-03-26Watts says investigating why the windowing was so sensitive showed how many taps are needed before it stops mattering: ten to the power of seventeen. Eric's Hi-Fi 4:45
• 2023-03-26Watts says he was the first to talk about large tap counts, but what matters is the algorithm itself, not the taps. Eric's Hi-Fi 9:13
• 2023-03-26Watts says thousands of listening tests tuned the five windowing variables to 10 parts per million, rechecking each, using four or five tracks for different sound parameters. Eric's Hi-Fi 9:32
• 2023-04-03Watts says what else has gone into it matters more, because it is not just about taps but about the algorithm itself. Amplify Audio 2:49
• 2023-07-01Watts says the WTA algorithm cannot be reverse engineered, as the FPGA detects impulses, and its 5 variables are tuned to 10 parts per million through thousands of listening tests. Head-Fi, Jul 2023
• 2023-09-20Watts describes tuning WTA variables to about 100ppm with dedicated test tracks, notes Hugo 2's warm settings remove WTA2, and says Mojo 2's UHD DSP adds warmth without timing loss. Head-Fi, Sep 2023
• 2024-05-10Watts says he did not understand why his window function was so sensitive to 10 parts per million, and now understands exactly what is going on. Reactcore 1:25
• 2024-05-16Watts says all interpolation filters distort; the key is minimal distortion and the right algorithm, and thousands of listening tests on WTA let it reconstruct more accurately. The Speaker Shack 3:02
• 2024-05-17Watts says the work involved much experimentation fine-tuning the algorithm, and that the device contains two and a half thousand discrete components. needs context AVstore 1:00
• 2024-05-17Watts says the algorithm matters much more than the number of taps, and it has been optimized to reconstruct timing much more accurately than before. AVstore 4:40
• 2024-07-12Watts says with finite taps the coefficient recipe matters; the WTA algorithm has five variables, each tuned by listening to minimize timing error as the brain perceives it. HIFICLUB 12:16
• 2024-07-12Watts lists what he listens for (separation, timbre variation, soundstage focus and depth, note starts and stops) with many test tracks, adjusting each variable to an optimum. HIFICLUB 13:09
• 2024-07-12Watts says thousands of listening tests found the WTA variables' sweet spot, which suits everyone's brain, and the work has been more taps plus tuning toward 16-bit performance. HIFICLUB 13:56
• 2024-07-12Watts says theory only gives pointers and his filters are set by sound-quality tests, unlike other upsamplers whose coefficients come from maths; he aims for neither warm nor bright. HIFICLUB 15:30
• 2024-07-12Watts says the code is partly control code and partly filter coefficient values that must each be put into the FPGAs, adding up to over two million lines. needs context HIFICLUB 50:09
• 2024-08-01Watts says better sound needs both the unique WTA algorithm, developed over many years with thousands of listening tests, and large FPGA computing capacity, summarizing his FPGA approach's benefits. Audiophilesdoteu 5:27
• 2024-09-29Watts says listening tests showed he needed far greater filter coefficient accuracy, so he computed at 40 decimal places with aggressive noise shaping but could not verify performance. The Source AV 6:30
• 2024-09-29Watts says his son wrote an FFT algorithm from first principles; at a thousand-digit resolution distortion and noise were at 3,500 dB, proving the tool and computation correct. The Source AV 7:12
• 2024-09-29Watts says running the coefficients through the new tool showed results nothing like expected because his coefficient tools were flawed, so he changed the tool set for much better precision. The Source AV 8:53
• 2024-09-29Watts says that with new coefficients and a different calculation routine, the subjectively optimized numbers came out the same, a relief confirming his listening was correct. The Source AV 9:50
• 2024-10-02Watts says a new unlimited-precision FFT showed his old coefficients were wrong; corrected ones kept the same preferred settings, improved sound, and delayed everything 3 months. Head-Fi, Oct 2024
• 2025-02-17Watts says perception can only be judged by listening tests; the WTA algorithm uses his own windowing formula with five variables, and tweaking them changes the sound. audio-2G 7:28
• 2025-02-17Watts says WTA variables were tuned by listening down to 10 parts per million, that many listeners wrongly hear brightness as accuracy, and that he aims for the original sound. audio-2G 8:13
• 2025-02-17Watts says different recordings do not need different optimal settings because reconstruction error is fundamental; he uses three or four test recordings per parameter, such as depth. audio-2G 10:31
• 2025-05-12Watts says finding the best-sounding FIR filter took him over 40 years; theory requires all coefficients to be sinc, but using only sinc in an interpolation filter causes a problem. Audiophile Junkie 8:14
• 2025-05-12Watts says a pure sinc filter jumps abruptly from zero to full sinc at its start, and that abrupt change itself creates audible transient timing errors. Audiophile Junkie 8:55
• 2025-05-12Watts says conventional filters taper sinc coefficients for measured performance, causing audible timing errors whatever the tap count, so the coefficient algorithm matters greatly, and traditional algorithms skip listening tests. Audiophile Junkie 9:19
• 2025-05-12Watts says conventional design ignores transient timing recovery, and his WTA algorithm avoids the abrupt start while keeping the maximum number of coefficients at ideal sinc values. Audiophile Junkie 10:04
• 2025-05-12Watts says WTA's five variables, optimized over 25 years with thousands of listening tests, were tuned by ear to ten parts per million (0.001%); over half the coefficients are sinc. Audiophile Junkie 10:46
• 2025-05-12Watts lists further test criteria (tonal colors, low-frequency pitch, dynamics, rhythm and flow, separation and focus, note starts and stops, clarity) that he scored before adjusting the filter. Audiophile Junkie 12:30
• 2025-05-12Watts says he adjusted the coefficients to hit a sweet spot that always existed, sometimes going back to redo other variables, calling it an intense process. Audiophile Junkie 13:15
• 2025-05-12Watts lists tap counts: DAC64 1,000 (1999), QBD 18 thousand, Hugo 26 thousand (2013), DAVE 164 thousand, Hugo M Scaler 1 million; more taps and WTA improvements each improved sound. Audiophile Junkie 13:35
• 2026-03-24Watts says Quartet began as a better Hugo M Scaler but became a study of interpolation filters; his unique WTA algorithm was tuned through thousands of listening tests. Audio Force 9:47
• 2026-03-24Watts says each of the WTA equation's five factors had to be set by ear to within ten parts per million, and he did not understand why a million taps was so sensitive. Audio Force 10:45
• 2026-03-24Watts says conventional interpolation filters in high-end DACs always get transient timing slightly early or late, and the WTA filter reduces that timing uncertainty. Audio Force 12:35
• 2026-03-24Watts says he found two different factors change transient timing, and with a standard interpolation filter improving one degrades the other. Audio Force 13:07
• 2026-03-24Watts says the ideal is impossible with a standard filter, so he developed a completely new type of interpolation filter called Blackbird WTA. Audio Force 13:51
• 2026-03-24Watts says Blackbird WTA optimizes both factors independently, giving a 10 times improvement in sound quality, the primary difference between Quartet and his earlier work. Audio Force 14:13
• 2026-05-03Watts says sampled digital audio, with samples 22 microseconds apart on CD, reproduces transient timing poorly; the interpolation filter reconstructs it, and he has spent 30 years developing WTA. Audio Force 6:49
• 2026-05-03Watts says the algorithm is much more important than the number of taps. Audio Force 8:03
• 2026-05-03Watts says the WTA algorithm alone is designed for transient timing accuracy, unlike filters built for frequency response or stopband; for a given algorithm, doubling taps halves timing error. Audio Force 8:16
• 2026-08-30Watts says that after the Hugo M Scaler, more taps (1,000 in 1999) and a better WTA kept sounding better; a million taps gives 16-bit reconstruction, but more is needed. The Source AV 6:00
• 2026-08-30Watts says a single-stage filter trades off two problems like a seesaw; his Blackbird WTA solves each in turn, a new structure cutting the delay to tens of seconds. The Source AV 8:23
• 2026-08-30Watts says the approach is radically different and he is super excited by the sound quality they are getting from Quartet. needs context The Source AV 9:14
• 2026-10-11Watts says Quartet took longer because his son Daniel built unlimited-precision coefficient tools; a test sine computed to 3,000 decimal places showed distortion and noise about 3 thousand dB down. Distorsiuni Interioare 8:25
• 2026-10-11Watts says the new tools let them see incredibly small effects, change coefficients and listen, which opened a can of worms. Distorsiuni Interioare 9:20
• 2026-10-11Watts says his research from 2018 asked how many taps give subjectively perfect reconstruction, and why his five-variable WTA coefficient formula had a sweet spot. Distorsiuni Interioare 17:04
• 2026-10-11Watts says raising a variable improved sound until it got worse; each of the five variables had a sweet spot within ten parts per million, audible in careful listening tests. Distorsiuni Interioare 17:52
• 2026-10-11Watts says after a couple of years of research he found two different factors degrading transient reconstruction accuracy. Distorsiuni Interioare 18:37
• 2026-10-11Watts says the WTA filter handles two conflicting factors together, and that the taps needed came to 4 with twenty-six zeros, with a delay of 900 trillion years. Distorsiuni Interioare 19:19
• 2026-10-11Watts says that delay is 66 thousand times the universe's lifetime, so tap length could not keep growing; his Blackbird WTA processes the two factors separately. Distorsiuni Interioare 20:07
• 2026-10-11Watts says Blackbird gives at least a tenfold improvement on one factor by using ideal sinc values, and unlimited-precision mathematics let him eliminate the other factor's error. Distorsiuni Interioare 20:50
• 2026-10-11Watts says the equivalent requirement fell from 900 trillion years to seconds or tens of seconds, so the improvement exceeds an order of magnitude. Distorsiuni Interioare 21:37
• 2026-10-11Watts says the key issue is the algorithm; nobody discusses transient reconstruction or tuning filters thousands of times, and he gives customers one listening-optimized solution, not many options. Distorsiuni Interioare 38:03
• 2026-10-14Watts says more taps approach an ideal sinc, but the algorithm matters far more: a billion taps with the wrong algorithm would sound worse than a thousand. Part-Time Audiophile 30:14
• 2026-10-14Watts says the coefficient algorithm matters most, but with a given algorithm, doubling the taps and adjusting accordingly improves sound quality. Part-Time Audiophile 30:58
• 2026-10-14Watts says ESS chips have half a dozen filters and at most a few hundred taps, versus 4 million on Quartet and, he thinks, about 44 thousand on Mojo 2. Part-Time Audiophile 33:10
• 2026-10-14Watts says his filters were designed from listening tests, thinking and experiments to remove or minimize the transient timing problem. Part-Time Audiophile 34:01
• 2026-10-14Watts says Quartet began about 8 years ago after the 1 million tap Hugo M Scaler, which guarantees 16-bit accurate reconstruction; 6 years of research went into improving interpolation filters. Part-Time Audiophile 52:36
• 2026-10-14Watts says the algorithm was radically improved, and they are calling it a Blackbird WTA. Part-Time Audiophile 53:23
• 2026-10-17Watts describes tuning the five WTA equation variables to within 10 parts per million by listening, finding a sweet spot with the million taps. article, Oct 2026
• 2026-10-17Watts says two contrary effects degrade transient timing in the WTA filter and in all interpolation filters, so improving one worsens the other in a single-stage filter. article, Oct 2026
• 2026-10-17Watts says separating the two problems into different filters, each optimized, led to the Blackbird WTA structure. article, Oct 2026
• 2026-10-17Watts says Blackbird WTA improves sinc reconstruction accuracy tenfold, eliminates the other problem and cuts the delay from 900 trillion years to tens of seconds; the algorithm, not four million taps, is the story. article, Oct 2026
• 2026-10-17Watts says generating coefficients takes forever even on his very fast PC, which is why he is skeptical. article, Oct 2026
• 2026-10-17Watts says the FPGA gives needed precision and a direct FIR filter without FFT tricks, and the algorithm matters far more than tap count, as Blackbird and WTA show. article, Oct 2026